%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM042-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:17:52 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 21 ( 14 unt; 0 def)
% Number of atoms : 29 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 23 ( 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
fof(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inverse) ).
fof(f122,axiom,
! [X0] : union(X0,inverse(X0)) = symmetrization_of(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',symmetrization) ).
fof(f124,axiom,
! [X0,X1] :
( ~ subclass(restrict(X0,X1,X1),complement(identity_relation))
| irreflexive(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',irreflexive2) ).
fof(f176,negated_conjecture,
subclass(x,complement(identity_relation)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_irreflexive_class_property4_1) ).
fof(f177,negated_conjecture,
~ irreflexive(x,domain_of(symmetrization_of(x))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_irreflexive_class_property4_2) ).
fof(f191,plain,
! [X0] : symmetrization_of(X0) = complement(intersection(complement(X0),complement(domain_of(flip(cross_product(X0,universal_class)))))),
inference(definition_unfolding,[],[f122,f26,f39]) ).
fof(f245,plain,
! [X0,X1] :
( irreflexive(X0,X1)
| ~ subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation)) ),
inference(definition_unfolding,[],[f124,f28]) ).
fof(f268,plain,
~ irreflexive(x,domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))),
inference(definition_unfolding,[],[f177,f191]) ).
fof(f328,plain,
! [X0] :
( member(X0,complement(identity_relation))
| ~ member(X0,x) ),
inference(resolution,[],[f1,f176]) ).
fof(f426,plain,
~ subclass(intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))),complement(identity_relation)),
inference(resolution,[],[f245,f268]) ).
fof(f427,plain,
~ member(not_subclass_element(intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))),complement(identity_relation)),complement(identity_relation)),
inference(resolution,[],[f426,f3]) ).
fof(f428,plain,
member(not_subclass_element(intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))),complement(identity_relation)),intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),
inference(resolution,[],[f426,f2]) ).
fof(f432,plain,
~ member(not_subclass_element(intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))),complement(identity_relation)),x),
inference(resolution,[],[f427,f328]) ).
fof(f462,plain,
member(not_subclass_element(intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))),complement(identity_relation)),x),
inference(resolution,[],[f428,f21]) ).
fof(f467,plain,
$false,
inference(forward_subsumption_resolution,[],[f462,f432]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM042-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 18:42:34 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.41 Running first-order model finding
% 0.16/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.49 % (3333999)Will run a generic schedule for satisfiability detection.
% 0.16/0.49 % (3334011)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4273649769:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.49 % (3334006)% WARNING: option uhcvi not known.
% 0.16/0.49 % (3334010)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1006775213:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.49 % (3334005)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1943031247_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.49 % (3334006)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1462420607:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.49 % (3334008)dis+10_1_sil=32000:sp=arity:random_seed=898486937:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.49 % (3334009)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1139919661:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.49 % (3334009) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3333999-3334009"...
% 0.16/0.50 % (3334009)...printing done.
% 0.16/0.50 % (3334009)Refutation found. Thanks to Tanya!
% 0.16/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.50 % (3334009)------------------------------
% 0.16/0.50 % (3334009)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (3334009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (3334009)CaDiCaL version: 2.1.3
% 0.16/0.50 % (3334009)Termination reason: Refutation
% 0.16/0.50 % (3334009)Time elapsed: 0.024 s
% 0.16/0.50 % (3334009)Peak memory usage: 12 MB
% 0.16/0.50 % (3334009)Instructions burned: 22 (million)
% 0.16/0.50 % (3333999)Success in time 0.069 s
% 0.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------